The Topology of the Space of Holomorphic Maps with Bounded Multiplicity

Abstract

For a complex (quasi-) projective variety X CP N with π 2 (X) = Z and an integer d ≥ 0, let Hol * d (S 2 , X) denote the space consisting of all basepoint preserving holomorphic maps f from S 2 to X with degree d. We study the topology of certain subspaces of Hol